There is one Catholic Mass for the Dead. It is not strictly speaking called a “Requiem” Mass, but in Latin, Liturgia defunctorunm: missae pro defunctis (Liturgy of the dead: Mass for the dead).
The Requiem is only one option, but the best-known one, for the Introit. There are a total of seven possible introits that can be licitly used, in the Graduale Romanum. The others are:
De necessitatibus meis eripe me; Ps 24, introit for Friday in the first week of Lent
Ego autem cum iustitia apparebo; Ps 16 from Thursday of the second week of Lent
Intret oratio mea in conspectu tuo; Ps 87 from the 32nd Sunday in Ordinary Time (coming up tomorrow at the abbey!)
Si iniquitatis observaveris, Domine; Ps 129 from the 28th Sunday in OT
Sicut oculi servorum in manibus; Ps. 122 from the first Monday in Lent
Verba mea auribus percipe, Domine. Ps. 5 from the first Thursday in Lent.
All psalms numbered according to the Vulgate.
Only one, “Requiem in aeternam” is proper to the Mass for the dead. The others are all used at various other Masses. In Eastertide, only one Introit is prescribed: Ecce oculi Domini (Ps 32)
The Liturgy of the dead includes the Mass of course, but also the vigil with the deceased, first station at the home of the deceased, procession into the church, second station: in the church (the Mass for the dead), the procession to the cemetery, and third station at graveside. It’s unlikely that most will ever experience more than the Mass for the dead unless one is the pope or a cardinal!
These are all described in the 1974 Graduale Romanum which is the official chant book for Gregorian chant in the post-Conciliar church.
If I could have Gregorian chant for my whole funeral Mass, I would love it…but that ain’t going to happen.
It is possible if you have your funeral in Sherbrooke, QC, where the Gregorian schola I sing with will gladly do your funeral in Gregorian chant for a very modest stipend. We have in fact done many. I like to say “we sing at funerals and a wedding” because we’ve sung at many funerals, but only 1 wedding in the 16 years I’ve been singing with them (and that’s cheating: it was the wedding of the daughter of one of our choristers, but I digress). We’ll even add the Dies Irae if you request it and the pastor allows it…
Personally I want chant at my funeral as well! I’d choose, from the options:
IN: Requiem in aeternam
GR: Laetatus sum (Ps. 121: I was glad when they said to me,
“Let us go to the house of the Lord!”)
AL: In Exitu Israel ex Aegypto (Ps,. 113)
TR (if I die during Lent): De profundis (ps. 129)
OF: De profundis (Ps. 129)
CO: Lux aeterna (IV Esdr.) or Qui Manducat (John 6:57)